arXiv subjects

Yunong Zhou

Publications and source records attributed to Yunong Zhou.

6 recordsLinked to original sources

arXiv2026

Stochastic process model of rough surface contact

The stochastic process model of rough surface contact, widely known as Persson's theory of contact, serves as a representative multi-scale model that has been extensively applied across various fields of tribology. In this chapter, we briefly introduce the background of the development of Persson's theory of contact. We thoroughly discuss Persson's theory for purely normal elastic contact, with a special focus on solving the probability density of the contact pressure and the interfacial gap using partial differential equations. Subsequent applications of these fundamental results in addressing more complex interfacial properties in other fields of tribology are also examined. Finally, several recommendations regarding future studies of Persson's theory are proposed. This review article is expected to assist researchers in quickly familiarizing themselves with the current state of the art of Persson's theory and to attract more attention from tribologists and solid mechanicians, thereby contributing to the development and application of Persson's theory of contact.

cond-mat.soft↗

arXiv2026

Mass weighting algorithm optimizes Fourier-based physics-informed neural network in adhesive contact mechanics

Physics-informed neural networks (PINNs) for elastic contact mechanics suffer from a spectral stiffness imbalance,that is, the elastic kernel grows linearly with wave number, causing short-wavelength modes to dominate gradient updates and stall convergence of the macroscopic deformation. We introduce a spectral preconditioning strategy that reweights displacement gradients in Fourier space before back-propagation, amplifying low wavenumber components through a mass weighting (MW) function while suppressing sub-grid noise via a built-in low-pass filter. Applied to adhesive line contact problems, the mass weighted PINN reaches machine-zero residual loss within 400 Adam iterations for specified benchmark, whereas the reference benchmark stalls at three orders of magnitude higher loss. The converged displacement and contact stress fields agree quantitatively with Green's function molecular dynamics (GFMD) solutions for both smooth Hertz contact at pressures spanning tension to compression and rough surfaces with roughness covering several decades of wavelength. The method operates directly on a uniform real-space grid, requires no explicit Green's function integration or quadrature rules, and is formulated entirely in terms of minimising a scalar energy function. Extension to two-dimensional rough surfaces is direct, as both the Fourier elastic energy and the spectral preconditioner depend only on the wave-number magnitude.

cond-mat.soft↗

arXiv2026

Field-theoretical approach to estimate mean gap and gap distribution in randomly rough surface contact mechanics

We extend the statistical field-theoretical framework of rough surface contact mechanics to characterize the interfacial gap between an elastic half-space and a randomly rough surface incorporating exponential repulsion. Building upon a cumulant expansion to second-order, we derive an explicit analytical relation between the mean gap and the applied normal pressure. This result provides a closed-form expression for the drift and diffusion coefficients in a convection-diffusion equation governing the scale-dependent evolution of the gap distribution. Solving this equation with appropriate initial and boundary conditions yields the gap distribution under varying external pressures. Both the mean gap and the gap distribution are found to be in good agreement with Green's function molecular dynamics (GFMD) simulations. Our results demonstrate that the field-theoretical approach enables quantitative predictions not only for contact stresses but also for interfacial gap in rough surface contacts.

cond-mat.soft↗

arXiv2025

Persson's Theory of Purely Normal Elastic Rough Surface Contact: A Tutorial Based on Stochastic Process Theory

Persson's theory of purely normal rough surface contact was developed two decades ago during the study of tire-road interaction, and gradually became one of the dominant approaches to study the solid-solid interaction between rough surfaces. Contrary to its popular applications in various cross-disciplinary fields, the fundamental study of Persson's theory of contact attracted little attention from the tribology and contact mechanics communities. As far as the authors know, many researchers struggle to understand the derivation of the theory. Few attempts have been made to clarify the oversimplified derivation provided by Persson (Persson, 2001). The present work provides a detailed tutorial on Persson's theory, which does not simply follow the commonly adopted derivation initiated by Persson. A new derivation is given based on stochastic process theory, assuming that the variation of the random contact pressure with respect to scale is a Markov process. We revisit the essential assumptions utilized to derive the diffusion equation, boundary conditions, drift and diffusion coefficients, and closed-form results. This tutorial can serve as a self-consistent introduction for solid mechanicians, tribologists, and postgraduate students who are not familiar with Persson's theory, or who struggle to understand it.

cond-mat.stat-mech↗

arXiv2025

Revisiting the diffusion equation derivation in Persson's theory of contact

In Persson's seminal work on tire-road interaction (Persson, J. Chem. Phys. {\bf 115}(8), 2001), he ingeniously derived a diffusion equation in Appendix B to characterize the evolution of contact pressure between a rigid rough indenter and an elastic half-space with spatial magnification, which constitutes the foundation of Persson's theory of contact. Persson's theory has been extensively validated and applied to investigate nearly all critical aspects of tribological problems. In contrast to the well-known Greenwood-Williamson (GW) model, Persson's theory receives relatively less attention within the tribology community. One contributing factor to this discrepancy is that the original derivation of the diffusion equation in Appendix B is not easily understandable to non-physicists. In this technical note, the authors provide supplementary information for each step of the derivation, aiming to clarify the conceptual foundation for researchers who encounter difficulties in understanding Persson's theory, thereby encouraging its broader application within and beyond tribology.

cond-mat.soft↗

arXiv2024

Stochastic process model for interfacial gap of purely normal elastic rough surface contact

In purely normal elastic rough surface contact problems, Persson's theory of contact shows that the evolution of the probability density function (PDF) of contact pressure with the magnification is governed by a diffusion equation. However, there is no partial differential equation describing the evolution of the PDF of the interfacial gap. In this study, we derive a convection--diffusion equation in terms of the PDF of the interfacial gap based on stochastic process theory, as well as the initial and boundary conditions. A finite difference method is developed to numerically solve the partial differential equation. The predicted PDF of the interfacial gap agrees well with that by Green's Function Molecular Dynamics (GFMD) and other variants of Persson's theory of contact at high load ranges. At low load ranges, the obvious deviation between the present work and GFMD is attributed to the overestimated mean interfacial gap and oversimplified magnification-dependent diffusion coefficient used in the present model. As one of its direct application, we show that the present work can effectively solve the adhesive contact problem under the DMT limit. The current study provides an alternative methodology for determining the PDF of the interfacial gap and a unified framework for solving the complementary problem of random contact pressure and random interfacial gap based on stochastic process theory.

cond-mat.soft↗